Basic Math Examples

4 \frac{1}{2} \cdot 2 \frac{1}{4}

$4 \frac{1}{2} \cdot 2 \frac{1}{4}$

Step 1

Convert

4 \frac{1}{2}

$4 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

(4 + \frac{1}{2}) \cdot 2 \frac{1}{4}

$(4 + \frac{1}{2}) \cdot 2 \frac{1}{4}$

Step 1.2

Add

4

$4$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

(4 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 2 \frac{1}{4}

$(4 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 2 \frac{1}{4}$

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{4 \cdot 2}{2} + \frac{1}{2}) \cdot 2 \frac{1}{4}

$(\frac{4 \cdot 2}{2} + \frac{1}{2}) \cdot 2 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{4 \cdot 2 + 1}{2} \cdot 2 \frac{1}{4}

$\frac{4 \cdot 2 + 1}{2} \cdot 2 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

2

$2$ .

\frac{8 + 1}{2} \cdot 2 \frac{1}{4}

$\frac{8 + 1}{2} \cdot 2 \frac{1}{4}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{2} \cdot 2 \frac{1}{4}

$\frac{9}{2} \cdot 2 \frac{1}{4}$

\frac{9}{2} \cdot 2 \frac{1}{4}

$\frac{9}{2} \cdot 2 \frac{1}{4}$

\frac{9}{2} \cdot 2 \frac{1}{4}

$\frac{9}{2} \cdot 2 \frac{1}{4}$

\frac{9}{2} \cdot 2 \frac{1}{4}

$\frac{9}{2} \cdot 2 \frac{1}{4}$

Step 2

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

\frac{9}{2} \cdot (2 + \frac{1}{4})

$\frac{9}{2} \cdot (2 + \frac{1}{4})$

Step 2.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{9}{2} \cdot (2 \cdot \frac{4}{4} + \frac{1}{4})

$\frac{9}{2} \cdot (2 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{9}{2} \cdot (\frac{2 \cdot 4}{4} + \frac{1}{4})

$\frac{9}{2} \cdot (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{9}{2} \cdot \frac{2 \cdot 4 + 1}{4}

$\frac{9}{2} \cdot \frac{2 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{9}{2} \cdot \frac{8 + 1}{4}

$\frac{9}{2} \cdot \frac{8 + 1}{4}$

Step 2.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{2} \cdot \frac{9}{4}

$\frac{9}{2} \cdot \frac{9}{4}$

\frac{9}{2} \cdot \frac{9}{4}

$\frac{9}{2} \cdot \frac{9}{4}$

\frac{9}{2} \cdot \frac{9}{4}

$\frac{9}{2} \cdot \frac{9}{4}$

\frac{9}{2} \cdot \frac{9}{4}

$\frac{9}{2} \cdot \frac{9}{4}$

Step 3

Multiply

\frac{9}{2} \cdot \frac{9}{4}

$\frac{9}{2} \cdot \frac{9}{4}$ .

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Step 3.1

Multiply

\frac{9}{2}

$\frac{9}{2}$ by

\frac{9}{4}

$\frac{9}{4}$ .

\frac{9 \cdot 9}{2 \cdot 4}

$\frac{9 \cdot 9}{2 \cdot 4}$

Step 3.2

Multiply

9

$9$ by

9

$9$ .

\frac{81}{2 \cdot 4}

$\frac{81}{2 \cdot 4}$

Step 3.3

Multiply

2

$2$ by

4

$4$ .

\frac{81}{8}

$\frac{81}{8}$

\frac{81}{8}

$\frac{81}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{81}{8}

$\frac{81}{8}$

Decimal Form:

10.125

$10.125$

Mixed Number Form:

10 \frac{1}{8}

$10 \frac{1}{8}$